The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is extended to dynamical problems. The auto-correlation functions of the Transverse Ising chain are derived by this method. It is shown that the Trotter-directional correlatio
n function is interpreted as a Matsubaras temperature Green function and that the auto-correlation function is given by analytic continuation of the Green function. We propose the Trotter-directional correlation function is a new measure of the quantum fluctuation and show how it works well as a demonstration.
We performed phase-reference very long baseline interferometry (VLBI) observations on five radio-loud narrow-line Seyfert 1 galaxies (NLS1s) at 8.4 GHz with the Japanese VLBI Network (JVN). Each of the five targets (RXS J08066+7248, RXS J16290+4007,
RXS J16333+4718, RXS J16446+2619, and B3 1702+457) in milli-Jansky levels were detected and unresolved in milli-arcsecond resolutions, i.e., with brightness temperatures higher than 10^7 K. The nonthermal processes of active galactic nuclei (AGN) activity, rather than starbursts, are predominantly responsible for the radio emissions from these NLS1s. Out of the nine known radio-loud NLS1s, including the ones chosen for this study, we found that the four most radio-loud objects exclusively have inverted spectra. This suggests a possibility that these NLS1s are radio-loud due to Doppler beaming, which can apparently enhance both the radio power and the spectral frequency.
